Method and apparatus for producing three dimensional shapes

ABSTRACT

A method and system for automatically producing data representative of a modified head shape from data representative of a deformed head is provided. The method includes a step of processing captured data for the deformed head utilizing Principal Component Analysis (PCA) to generate PCA data representative of the deformed head. The method also includes the steps of providing the PCA data as input to a neural network; and utilizing the neural network to process the PCA data to provide data representative of a corresponding modified head shape.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a division of application Ser. No. 10/753,012 filedJan. 7, 2004 now U.S. Pat. No. 7,305,369. The following related patentapplications were filed on even date therewith and are assigned to acommon assignee: Ser. No. 10/753,013 Cranial Remodeling Device Databaseby T. Littlefield and J. Pomatto now U.S. Pat. No. 7,177,461: Ser. No.10/753,118 Automatic Selection of Cranial Remodeling DeviceConfiguration by T. Littlefield and J. Pomotto now U.S. Pat. No.7,242,798: Ser. No. 10/753,006 Automatic Selection of Cranial RemodelingDevice Trim Lines by T. Littlefield and J. Pomatto now U.S. Pat. No.7,127,101: and Ser. No. 10/752,800 Cranial Remodeling DeviceManufacturing System by T. Littlefield, and J. Pomatto now U.S. Pat. No.7,142,701. The disclosures of the above-identified applications areincorporated herein.

FIELD OF THE INVENTION

This invention pertains to a system and method for producing datarepresentative of desired three dimensional shapes from correspondingdata representative of first three dimensional shapes, in general, andto a system and method for automatically producing data representativeof a modified three dimensional head shapes from corresponding datarepresentative of a deformed head shape.

BACKGROUND OF THE INVENTION

Cranial remodeling is utilized to correct for deformities in the headshapes of infants. Prior to the development of the Dynamic OrthoticCranioplasty^(SM) method of cranial remodeling by Cranial Technologies,Inc, the assignee of the present invention, the only viable approach forcorrection of cranial deformities was surgical correction of the shapeof the cranium. Dynamic Orthotic Cranioplasty^(SM) utilizes a treatmentprogram in which a cranial remodeling band is custom produced for eachinfant to be treated. The band has an internal shape that produces thedesired shape of the infant□s cranium.

In the past, the cranial remodeling band was produced by first obtaininga full size and accurate model of the infants actual head shape. Thisfirst model or shape was then modified to produce a second or desiredhead shape. The second or desired head shape is used to form the cranialremodeling band for the infant. The first shape was originally producedas a cast of the infant□s head. The second shape was similarly producedas a cast of the head. In the past the second or desired shape wasobtained by manually modifying the first shape to form the desiredshape.

Various arrangements have been considered in the past to automate theprocess of producing cranial remodeling devices. In some of the priorarrangements a scanner is utilized to obtain three dimensional data ofan infant□s head. Such arrangements have the disadvantage in thatscanners cannot obtain instantaneous capture of data of the entirety ofan infant□s head. In addition, it is proposed to utilize expert systemsto operate on scanned data to produce an image of a modified head shapefrom which a cranial remodeling device may be fabricated. However,because each head shape is unique, even the use of an expert system maynot present an optimized solution to developing modified shapes suitablefor producing a cranial remodeling device.

SUMMARY OF THE INVENTION

In accordance with the principles of the invention, a method forautomatically producing data representative of a desired head shape fromdata representative of a deformed head is provided. The method includesa step of processing captured data for the deformed head utilizingPrincipal Component Analysis (PCA) to generate PCA data representativeof the deformed head. The method also includes the steps of providingthe PCA data as input to a neural network; and utilizing the neuralnetwork to process the PCA data to provide data representative of acorresponding modified head shape.

In accordance with another aspect of the invention the method includestraining the neural network to generate data representative of deformedshapes to corresponding modified shapes

In the illustrative embodiment of the invention the captured datacomprises first data points represented as Cartesian coordinates. Thefirst data points are utilized to produce second data representative oflengths of rays of predetermined orientation.

The number of second data points is chosen to be a predetermined number,n. An n×n covariance matrix is computed. Eigenvalues and eigenvectorsare computed for the covariance matrix. The eigenvectors for apredetermined number of the largest eigenvalues are selected to definePCA shapes as the PCA data. In the illustrative embodiment thepredetermined number of the largest eigenvalues is 64.

A system for automatically producing data representative of a modifiedhead shape from data representative of a deformed head, in accordancewith the principles of the invention comprises one or more processorsoperable to process captured data for a deformed head utilizingPrincipal Component Analysis (PCA) to generate PCA data representativeof the deformed head. The one or more processors are further operated toprovide the PCA data as input to a neural network. The one or moreprocessors are operated to utilize the neural network to process the PCAdata to provide data representative of a corresponding modified headshape.

In accordance with one aspect of the invention the one or moreprocessors operates to train the neural network to generate datarepresentative of modified shapes for corresponding deformed shapes.

In one embodiment of the invention a first database comprises a firstplurality of first sets of captured data, each first set comprisingcaptured data for a corresponding one first head shape. A seconddatabase comprises a second plurality of second sets of captured data;each second set comprises captured data for a modified head shape for acorresponding one of the first head shapes. A processor is operable witha neural network program to train the neural network program with thefirst plurality of first sets of captured data and the second pluralityof second sets of captured data such that the neural network operates ona set of captured data for a first head shape to produce a correspondingmodified head shape.

In accordance with an aspect of the invention a support vector machineprogram is operated to train the neural network program. In theillustrative embodiment of the invention the support vector machinecomprises a least squares support vector machine.

In accordance with other aspects of the invention, the method andapparatus produce data representative of a modified three dimensionalshape from data representative of a first three dimensional shape.

In accordance with another aspect of the invention, a database for usein generating PCA coefficients and for training a neural networkcomprises a first plurality of first sets of captured data, eachcomprising captured data for a corresponding one first head shape; and asecond plurality of second sets of captured data each comprisingcaptured data for a modified head shape for a corresponding one of saidfirst head shapes.

In accordance with another aspect of the invention each first set ofcaptured data is obtained from a capture of a cast model of a first headshape. Each second set of captured data is obtained from a capture of acast model of a corresponding modified head shape.

In accordance with another aspect of the invention the captured data foreach first set of captured data comprises a plurality of Cartesiancoordinates each corresponding to a point on the corresponding one firsthead shape. The captured data for each second set of captured datacomprises a second plurality of Cartesian coordinates each correspondingto a point on a corresponding one modified head shape.

In accordance with another aspect of the invention, captured data foreach first set of captured data comprises a plurality of ray lengthsdefining the three dimensional shape of the corresponding first headshape. Captured data for each second set of captured data comprises aplurality of ray lengths defining the three dimensional shape of thecorresponding modified head shape.

In accordance with another aspect of the invention captured data of eachfirst set is converted from one coordinate system into data comprising aplurality of ray lengths defining the three dimensional shape.

BRIEF DESCRIPTION OF THE DRAWING

The invention will be better understood from a reading of the followingdetailed description taken in conjunction with the drawing figures inwhich like designations are utilized to identify like elements, and inwhich:

FIG. 1 illustrates steps in a method in accordance with the principlesof the invention:

FIG. 2 is a block diagram of a system in accordance with the principlesof the invention;

FIG. 3 illustrates use of Principal Components Analysis and neuralnetworks in the illustrative embodiment of the invention;

FIG. 4 illustrates steps in accordance with another aspect of theinvention;

FIG. 5 is table;

FIG. 6 represents a neural network;

FIG. 7 is a graph; and

FIG. 8 is a block diagram of a system in accordance with the principlesof the invention.

DETAILED DESCRIPTION

Turning to FIG. 1, steps 001 and 003 are steps that were utilized in thepast to produce a custom cranial remodeling device or band for an infantwith a deformed head. A positive life size cast is made of an infant□shead or a first shape as indicated at 001. A corresponding modified castor second shape is then made from which a cranial remodeling band isproduced at step 003. In the past, a cranial remodeling band for theinfant is produced by forming the band on the second cast whichrepresents a modified head shape. A library of hundreds of infant headcasts and corresponding modified casts has been maintained at theassignee of the present invention and this library of actual head castsand the corresponding modified casts is believed to be a uniqueresource. It is this unique resource that is utilized to providedatabases for developing the method and apparatus of the presentinvention.

An additional unique resource is that databases of additionalinformation corresponding to each infant have been developed by theassignee of the present invention. That database includes informationthat identifies the type of cranial remodeling device for each infanthead shape as well as the style of the cranial remodeling device andfeatures selected for incorporation into the cranial remodeling deviceto provide for appropriate suspension and correction of the deformity.Still further, each cranial remodeling device has trim lines that areuniquely cut so as to provide for appropriate suspension andfunctionality as well as appearance. A further database developed by theassignee of the present invention has trim line data for each cranialremodeling device that has been previously fabricated corresponding tothe casts for unmodified heads.

In a first embodiment of the invention, shown as system 200 in FIG. 2,the databases 203, 205 of unmodified shapes and corresponding modifiedshapes are used by a computer 201 to train a neural network 300.

In accordance with one aspect of the invention, each unmodified or firsthead shape is digitally captured at step 005 as shown in FIG. 1 by adigitizer 202 shown in FIG. 2, to produce first digital data at step 007to provide a complete three dimensional representation of the entiretyof a head including the top portion. The first digital data is stored indatabase 203 at step 009. Each corresponding modified or second headshape is digitally captured by digitizer 202 at step 011 to producesecond digital data at step 013. The second digital data is stored insaid database 205 at step 015. One to one correspondence is providedbetween each first digital data and the corresponding second digitaldata as indicated at step 017. The correspondence between digital datafor first and corresponding second head shapes is maintained byutilizing any one of several known arrangements for maintainingcorrespondence.

In accordance with one aspect of the illustrative embodiment the firstand second data stored comprises Cartesian coordinates for a pluralityof points on the surface of the corresponding shape.

In the illustrative embodiment shown in FIG. 1, digitizer 202 utilizes aplurality of digital cameras that are positioned to substantiallysurround the entirety of a cast or a patients head such that asubstantially instantaneous capture of the cast or of the infants headis obtained. As used herein, the term □digitizer□ is utilized toidentify any data capture system that produces digital data thatrepresents the entirety of a cast or a head and which is obtained from asubstantially instantaneous capture.

In accordance with an aspect of the illustrative embodiment of theinvention, neural network 300 is □trained□, as explained below, so thatcaptured data of a first or unmodified shape 301 shown in FIG. 3 whichhas no corresponding second or modified shape is processed by neuralnetwork 300 to produce a second or modified shape 303. Morespecifically, principal components analysis (PCA) is utilized inconjunction with neural network 300. Neural network 300 is trained byutilizing captured data for first shapes from database 203 withcorresponding captured data for second shapes from database 205.

Turning to FIG. 4, operation of system 200 is shown. At steps 401 and403, one or more databases are provided to store data for a plurality offirst or unmodified captured shapes and to store data for a plurality ofcorresponding second or modified captured shapes.

The data from each captured first and second image is represented usingthe same number of data points. In addition, all captured images areconsistently aligned with each other.

The captured data for all head shapes represented in the databases 203,205 of are aligned in a consistent way. The consistent alignment orimage orientation has two separate aspects: alignment of all capturedmodified images with each other as shown at step 405; and alignment ofeach unmodified captured image with the corresponding modified capturedimage as shown at step 407. Alignment of unmodified and modifiedcaptured images ensures that the neural network will consistently applymodifications. Alignment of the modified captured images with oneanother allows PCA to take advantage of the similarities betweendifferent cast shapes.

The casts from which the captured images are obtained do not includefacial details. Typically the face portion is merely a plane. Theposition of the face plane is really a result of deformity. To align theshapes a manually iterative visualization process is utilized. Thisapproach □solved□half of the alignment issue □aligning all of themodified images with each other so that the principal componentsanalysis could take advantage of the similarities between these shapes.

To align each unmodified captured image with its corresponding capturedmodified image, alignment of the face planes is was utilized. For themost part, the face planes represent a portion of the shapes that arenot modified from the unmodified to the modified head shape and provideconsistency. An additional attraction to this approach is that there onthe head actual casts, there is writing on the face planes and thiswriting is visible in the texture photographs that can be overlaid ontothe captured images. Alignment of face planes and writing provides aprecise registration of the unmodified and modified captured images.

An automated approach to this alignment was developed using several ofthe first captured images. The automated alignment works where texturephotographs are well focused and clear. In other cases automatedalignment is supplemented with alignment by selecting □freehand□ pointson both the modified and unmodified images using commercially availablesoftware and then using the registration tool of that software. Thisapproach aligned all unmodified captures with modified captures so thatcorrections would be consistently applied.

The capture data for both the unmodified and modified head shapes arenormalized at step 409 for training the neural network. As part of thenormalization, a scale factor is stored for each for each normalizedhead or shape set.

As indicated at step 411, PCA is utilized with the aligned shapes todetermine PCA coefficients. Because PCA uses the same set of basisvectors (shapes) to represent each head (only the coefficients in thesummation are changed), each captured image is represented using thesame number of data points. For computational efficiency, the number ofpoints should be as small as possible.

The original digitized data for first and second shapes stored indatabases 203, 205 represent each point on a surface using athree-dimensional Cartesian coordinate system. This approach requiresthree numbers per point; the x, y, and z distances relative to anorigin. In representing the head captures, we developed a scheme thatallows us to represent the same information using only one number perdata point. Mathematically the approach combines cylindrical andspherical coordinate systems. It should be noted that to obtain threedimensional representations of an object, a spherical coordinate systemmay be utilized. However, in the embodiment of the invention, the bottomof the shape is actually the neck of the infant, and is not of interest.

Conceptually this approach is similar to a novelty toy known as □a bedof nails.□ Pressing a hand or face against a grid of moveable pinspushes the pins out to form a 3D copy on the other side of the toy. Thisapproach can be thought of as a set of moveable pins protruding from acentral body that is shaped like a silo □ a cylinder with a hemispherecapped to the top. The pins are fixed in their location, except thatthey can be drawn into or out of the central body. Using this approach,all that is needed to describe a shape is to give the amount that eachpin is extended.

To adequately represent each head shape, a fixed number of approximately5400 data points are utilized. To represent each of the captures using afixed number of data points, the distance that each □pin□ protrudes iscomputed. This is easily achieved mathematically by determining thepoint of intersection between a ray pointing along the pin direction andthe polygons provided by data from the infrared imager. A set of such□pins□were selected as a reasonable compromise between accuracy of therepresentation and keeping the number of points to a minimum forefficiency in PCA. The specific set of points was copied from one of thelarger cast captures. This number was adequate for a large head shape,so it would also suffice for smaller ones. A commercially availableprogram used to execute this □interpolation□algorithm requires as inputthe original but aligned capture data and provides as output the set ofapproximately 5400 □pin lengths□ that represent the shape.

Using the consistent alignment and the consistent array of data pointsdescribed above, the normalized data for each captured cast wasinterpolated onto this □standard grid.□ Computing the covariance matrixproduced an n×n matrix, where □n□ is the number of data points. As thename implies, this covariance matrix analyzes the statisticalcorrelations between all of the □pin lengths.□ Computing the eigenvaluesand eigenvectors of this large covariance matrix provides PCA basisshapes. The PCA shapes are the eigenvectors associated with the largest64 eigenvalues of the covariance matrix. This approach of computingbasis shapes using the covariance matrix makes optimal use of thecorrelations between all the data points used on a standard grid.

PCA analysis allows cast shapes to be represented using only 64 PCAcoefficients. FIG. 5 sets out the hyper parameters for the 64 PCAcoefficients. To transform the unmodified cast shapes into correctmodified shapes, it is only necessary to modify the 64 PCA coefficients.For this processing task we selected and provide neural network 300 asindicated at step 413 of FIG. 4.

Neural networks are an example of computational tools known as □LearningMachines□and are able to learn any continuous mathematical mapping.

As those skilled in the art will understand, learning machines such asneural networks are distinguished from expert systems, in whichprogrammers are utilized to program a system to perform the samebranching sequences of steps that a human expert would perform. Ineffect, an expert system is an attempt to clone the knowledge base of anexpert, whereas, a neural network is taught to □think□or operate basedupon results that an expert might produce from certain inputs.

FIG. 6 shows a conceptual diagram of a generic neural network 300. At ahigh level, there are three elements of a neural network: the inputs,{acute over (α)}₁-{acute over (α)}_(n), the hidden layer(s) 603, and theoutputs β₁-β_(n). A neural network 300 operates on inputs 601 using thehidden layer to produce desired outputs 605. This is achieved through aprocess called □training.□

Neural network 300 is constructed of computational neurons eachconnected to others by numbers that simulate strengths of synapticconnections. These numbers are referred to as □weights.□

Training refers to modification of weights used in the neural network sothat the desired processing task is □learned□. Training is achieved byusing PCA coefficients for captured data representative of unmodifiedcasts of infant heads as inputs to the network 300 and modifying weightsof hidden layers until the output of the neural network matches PCAcoefficients for the captured data representative of correspondingmodified casts. Repeating this training thousands of times over theentire set of data representing the unmodified and correspondingcaptured shapes produces a neural network that achieves the desiredtransformation as well as is statistically possible. In the illustrativeembodiment, several hundred pairs of head casts were utilized to trainneural network 300 at step 415.

Testing on additional data from pairs of casts that the neural networkwas not trained with, or □verification testing□, was utilized in theillustrative embodiment to ensure that the neural network 300 haslearned to produce the appropriate second shape from first shapecaptured data and has not simply □memorized□the training set. Once thistraining of neural network 300 is complete, as measured by the averageleast squares difference between the PCA coefficients produced by thenetwork and those from the modified cast shapes, the PCA coefficientweights are □frozen□and the network is simply a computer program likeany other computer program and may be loaded onto any appropriatecomputer.

A commercially available software toolbox was used to develop thelearning machine. The particular type of learning machine produced iscalled a Support Vector Machine (SVM), specifically a Least SquaresSupport Vector Machine (LS-SVM). Just like the neural networks describedabove, the SVM □learns□ its processing task by modifying□weights□through a □training□process. But in addition to weights, theLS-SVM requires a user to specify □hyper parameters.□ For the radialbasis function (RBF) type of LS-SVM used in this work, there are twohyper parameters: ã (gamma) and ó (sigma). The relative values of theseparameters control the smoothness and the accuracy of the processingtask. This concept is very similar to using different degree polynomialsin conventional curve fitting.

FIG. 7 shows a curve-fitting task in two dimensions for easyvisualization. Because there are a finite number of data points, (x,y)-pairs, it is always possible to achieve perfect accuracy by selectinga polynomial with a high enough degree. The polynomial will simply passthrough each of the data points and bend as it needs to in between thedata where its performance is not being measured. This approach providesridiculous results in between the data points and is not a desiredresult. One solution to this problem is to require that the curvedefined by the polynomial be smooth i.e., to not have sharp bends. Thissolution is fulfilled in the LS-SVM using ã and ó. Higher values of ócorrespond to smoother curves and higher values of ã produce greateraccuracy on the data set.

An unmodified or first shape represented by captured data is processedutilizing a principal components analysis algorithm. The resulting PCArepresentation is processed by a neural network 300 to produce a secondor modified PCA representation of a modified shape.

In the system of the illustrative embodiment of the inventioncross-validation was used to choose the hyper-parameters. Data israndomly assigned to four groups. Three of the four groups were used totrain the LS-SVM, and the remaining set was used to measure theperformance in predicting the PCA coefficients for the modified headshapes. In turn, each of the four groups serves as the test set whilethe other three are used for training. The group assignment/division wasrepeated two times, so a total of eight training and test sets wereanalyzed (four groups with two repetitions). This process was repeatedfor a grid of (ã, ó)-pairs ranging from 0 □200 on both variables. Therange was investigated using a 70×70 grid of (ã, ó)-pairs, so a total of4900 neural nets were tested for each of the first 38 PCA coefficients.From this computationally intensive assessment, hyper-parameters weredetermined and validated for the first 38 PCA coefficients andextrapolated those results to select hyper-parameters for the remaining26. Further □tuning□ of the remaining 26 PCA hyper-parameters isunlikely to produce significant improvement in the final results becausethe first PCA coefficients are the most influential on the solution. Thetable shown in FIG. 5 presents the results for the hyper-parametertuning.

Once hyper parameters were tuned, the LS-SVM models generally producederrors of less than two percent for the PCA coefficients of the modifiedcasts in test sets (during cross-validation). Applying these tunedmodels to head casts that were not part of the cross-validation ortraining sets also generated excellent results.

There is a surprising variability of the head shapes as represented bycast shapes. Modified casts are not simply small changes to a consistent□helmet shape.□ Each is uniquely adapted to the unmodified shape that itis intended to correct. Being so strongly coupled to the unmodifiedshapes makes these modified casts surprisingly different from oneanother. Of the several hundred casts that we analyzed, each is unique.

Interpolating the aligned shapes also provided surprises and challenges.The □bed of nails□concept is very effective in reducing the size of thedata sets and providing a consistent representation for PCA. It helpsreduce the number of data sets that would have otherwise been requiredto train a larger neural network. Instead of representing each datapoint by three components, each data point is represented by onecomponent thereby reducing the number of data sets significantly. Byutilizing this approach, the process is speeded up significantly.

Returning to FIG. 4, at step 415, neural network 300 is trained asdescribed above. Once neural network 300 is trained, it is then utilizedto operate on new unmodified heads or shapes to produce a modified orsecond shape as indicated at step 417.

Turning now to FIG. 8, a block diagram of a system 800 in accordancewith the principles of the invention is shown. System 800 is utilized toboth train a neural network 300 described above and then to utilize thetrained neural network 300 to provide usable modified head shapes fromeither casts of deformed head shapes or directly from such an infant□shead.

System 800 includes a computer 801 which may any one of a number ofcommercially available computers. Computer 801 has a display 823 and aninput device 825 to permit visualization of data and control ofoperation of system 800.

Direct head image capture is a desirable feature that is provided toeliminate the need to cast the children□s head. An image capturingdigitizer 202 is provided that provides substantially instantaneousimage captures of head shapes. The digitized image 821 a is stored in amemory 821 by computer 801. Computer 801 utilizes a data conversionprogram 807 to normalize data, store the normalized data in memory 821and its scaling factor, and to convert the normalized, captured data to□bed of nails□data as described above. Computer 801 stores the modified,normalized data 821 b in memory 821. Computer 801 utilizing an alignmentprogram 809 to align modified data 821 b to an alignment consistent withthe alignments described above and to store the aligned data in anunmodified shapes database 803. Computer 801 obtains PCA coefficientsand weightings from a database 813 and utilizes neural network 300 and asupport vector machine 817 to operate on the data for a first shapestored in memory 821 a to produce data for a modified or second shapethat is then stored in memory 821 b. The data for the modified shapestored in memory 821 b may then be utilized to fabricate a cranialremodeling device or band for the corresponding head.

The invention has been described in terms of illustrative embodiments.It will be apparent to those skilled in the art that various changes andmodifications can be made to the illustrative embodiments withoutdeparting from the spirit or scope of the invention. It is intended thatthe invention include all such changes and modifications. It is alsointended that the invention not be limited to the illustrativeembodiments shown and described. It is intended that the invention belimited only by the claims appended hereto.

1. A method for automatically producing data representative of amodified head shape from data representative of a deformed head forutilization in a system for producing cranial remodeling devices,comprising: providing a neural network trained with a first plurality offirst sets of data, each said first set comprising captured data for acorresponding one first head shape, and with a second plurality ofsecond sets of captured data, each said second set comprising captureddata for a modified head shape for a corresponding one of said firsthead shapes; utilizing said neural network to operate on datarepresentative of a deformed head to produce data representative of amodified head shape; providing a computer readable memory; and storingsaid data representative of a modified head shape in said computerreadable memory for use in producing a cranial remodeling device.
 2. Amethod for automatically producing data representative of a modifiedhead shape from data representative of a deformed head, comprising:providing one or more computer readable memories comprising a firstdatabase and a second database; providing a neural network; providing tosaid neural network a first plurality of first sets of captured datafrom said first database, each said first set comprising captured datafor a corresponding one first head shape cast; providing to said neuralnetwork a second plurality of second sets of captured data from saidsecond database, each said second set comprising captured data for amodified head shape cast for a corresponding one of said first headshapes; training said neural network with said first plurality of firstsets of captured data and said second plurality of second sets ofcaptured data such that said neural network will operate on a set ofcaptured data for a first head shape to produce a new data set defininga unique modified head shape corresponding to said first head shape; andstoring said new data set as a third database in one of said one or morecomputer readable memories.
 3. A method in accordance with claim 2,comprising: providing a support vector machine; utilizing said supportvector machine to train said neural network.
 4. A method in accordancewith claim 3, wherein: said support vector machine comprises a leastsquares support vector machine.
 5. A system for automatically producingdata representative of a modified head shape from data representative ofa deformed head, comprising: a first database comprising a firstplurality of first sets of data, each said first set comprising data fora corresponding one first head shape; a second database comprising asecond plurality of second sets of data, each said second set comprisingcaptured data for a modified head shape for a corresponding one of saidfirst head shapes; a neural network program; and a processor operablewith said neural network program to train said neural network programwith said first plurality of first sets of data and said secondplurality of second sets of data such that said neural network operateson a set of data for a first deformed head shape to produce a data setdefining a unique corresponding modified head shape.
 6. A system inaccordance with claim 5, comprising: a support vector machine; said asupport vector machine program operable to train said neural networkprogram.
 7. A system in accordance with claim 6, wherein: said supportvector machine comprises a least squares support vector machine.
 8. Amethod for automatically producing data representative of a modifiedthree dimensional shape from data representative of a first threedimensional shape, comprising: providing a neural network; utilizingsaid neural network to operate on a first set of data representative ofa first shape to produce a second set of data corresponding to amodified three dimensional head shape; and storing said second set ofdata in a computer readable memory for utilization in forming a cranialorthosis.
 9. A method in accordance with claim 8, comprising: trainingsaid neural network with first plurality of first sets of data and saidsecond plurality of second sets of data such that said neural networkoperates on a set of captured data for a three dimensional shape toproduce a corresponding modified three dimensional shape.
 10. A methodin accordance with claim 9, comprising: providing a support vectormachine; and utilizing said support vector machine to train said neuralnetwork.
 11. A method in accordance with claim 10, wherein: said supportvector machine comprises a least squares support vector machine.